MOTION

Chapter Four: Motion 4.1 Position, Speed and Velocity 4.2 Graphs of Motion 4.3 Acceleration

4.2 Graphs of Motion Constant speed means the speed stays the same. An object moving at a constant speed always creates a position vs. time graph that is a straight line.

4.2 Graphs of Motion The data shows the runner took 10 seconds to run each 50-meter segment. Because the time was the same for each segment, you know the speed was the same for each segment.

4.2 Graphs of Motion You can use position vs. time graphs to compare the motion of different objects. The steeper line on a position vs. time graph means a faster speed.

4.2 Slope The slope of a line is the ratio of the “rise” to the “run”. The steepness of a line is measured by finding its slope.

Steepness of slope on Position-Time graph Steep slope = higher velocity Shallow slope = less velocity Downward slope = negative velocity Upward slope= positive velocity

Different Position. Vs. Time graphs Constant positive velocity (zero acceleration) Constant negative velocity (zero acceleration)

Position-Time Graph Java Applet

During which intervals was he traveling in a positive direction? During which intervals was he traveling in a negative direction? During which interval was he resting in a negative location? During which interval was he resting in a positive location? During which two intervals did he travel at the same speed? A) 0 to 2 sec B) 2 to 5 sec C) 5 to 6 sec D)6 to 7 sec E) 7 to 9 sec F)9 to 11 sec

4.2 Graphs of changing motion Objects rarely move at the same speed for a long period of time. A speed vs. time graph is also useful for showing the motion of an object that is speeding up or slowing down.

4.2 Graphs of changing motion Suppose we draw a rectangle on the speed vs. time graph between the x-axis and the line showing the speed. On the graph, the length is equal to the time and the height is equal to the speed. The area of the rectangle is equal to its length times its height.

Positive vs. Negative Is it possible to have a negative velocity and a positive acceleration? Is it possible to have a positive velocity and a negative acceleration? Is it possible to have a positive velocity and a positive acceleration? Is it possible to have a negative velocity and a negative acceleration?

Velocity & Acceleration Sign Chart + - Moving forward; Speeding up Moving backward; Slowing down Moving forward; Slowing down Moving backward; Speeding up

Constant Rightward Velocity

Constant Leftward Velocity

Constant Rightward Acceleration

Constant Leftward Acceleration

Leftward Velocity with Rightward Acceleration